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September 2003

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Benchmarks don't lie (TM)
by Richard B. Kreckel 28 Sep '03

28 Sep '03

Hi, AMD released the Opteron processor family today leaving people with the budget to buy new hardware wondering what exactly to purchase next. Here are some data to underpin your decision-making and convincing (whomever: head of department, parents, wife). I've let the suite of benchmarks from GiNaC-1.1.3 run on various machines, all clocked at 1.4 GHz, with one exception: the Itanium1 in the list was clocked at a mere 930MHz. Its timings were adjusted to accomodate for this difference in clock rates as far as possible. You'll notice anyway how that early silicon isn't worth being listed, it's just way slower than all the other machines. This has changed with the Itanium2. But apart from the two monsters M2 and N (with unconclusive results) it seems like the AMD chips generally perform faster than the Intel silicon. Naturally, all functions (except, perhaps, A, B and C) exercise some fairly jerky code with many branches. This is generally the case with CAS. Note that with the machines tested, the P-IV's handicap (its ridiculously large pipeline) was compensated by it having a comparatively fast DDR333, as opposed to the P-III which had less memory bandwith. Well, for such reasons the numbers below should be taken with a grain of salt. But still, my next personal machine won't be from Intel, and it won't be 32Bit either. So, without further ado, here are the numbers: Opteron Itanium2 Itanium1 P-III P-IV Athlon ------------------------------------------------------------------------------------------------------------ commutative expansion and substitution, size 200. 0.45s 0.55s 1.04s 0.63s 0.56s 0.53s commutative expansion and substitution, size 500. 3.43s 4.17s 7.78s 4.46s 4.25s 4.22s Laurent series expansion of Gamma function, order 20. 0.34s 0.43s 0.84s 0.57s 0.5s 0.36s Laurent series expansion of Gamma function, order 25. 1.37s 1.65s 3.27s 2.29s 2.01s 1.59s determinant of symbolic 10x10 Vandermonde matrix. 0.32s 0.37s 0.65s 0.45s 0.38s 0.27s determinant of symbolic 12x12 Vandermonde matrix. 2.99s 3.56s 6.07s 4.14s 3.48s 2.62s determinant of symbolic 8x8 Toeplitz matrix. 0.31s 0.37s 0.66s 0.43s 0.45s 0.27s determinant of symbolic 9x9 Toeplitz matrix. 1.25s 0.89s 2.59s 1.64s 1.88s 1.29s hash map size 500000 insert. 1.02s 1.16s 1.8s 1.01s 1.35s 1.15s hash map size 500000 find. 0.56s 0.69s 1.15s 0.63s 0.93s 0.62s hash map size 500000 erase. 0.43s 0.5s 0.85s 0.44s 0.66s 0.5s Lewis-Wester test A (divide factorials). 0.34s 0.357s 0.61s 0.38s 0.4s 0.43s Lewis-Wester test B (sum of rational numbers). 0.005s 0.008s 0.01s 0.006s 0.005s 0.004s Lewis-Wester test C (gcd of big integers). 0.059s 0.129s 0.16s 0.093s 0.116s 0.059s Lewis-Wester test D (normalized sum of rational fcns). 0.095s 0.136s 0.21s 0.135s 0.13s 0.083s Lewis-Wester test E (normalized sum of rational fcns). 0.07s 0.093s 0.16s 0.10s 0.098s 0.062s Lewis-Wester test F (gcd of 2-var polys). 0.009s 0.011s 0.021s 0.015s 0.011s 0.008s Lewis-Wester test G (gcd of 3-var polys). 0.27s 0.42s 0.65s 0.38s 0.43s 0.27s Lewis-Wester test H (det of 80x80 Hilbert). 1.37s 1.63s 2.45s 2.32s 2.08s 1.18s Lewis-Wester test I (invert rank 40 Hilbert). 0.38s 0.47s 0.73s 0.64s 0.56s 0.33s Lewis-Wester test J (check rank 40 Hilbert). 0.21s 0.28s 0.43s 0.34s 0.33s 0.18s Lewis-Wester test K (invert rank 70 Hilbert). 2.62s 3.24s 4.93s 4.28s 3.92s 2.31s Lewis-Wester test L (check rank 70 Hilbert). 1.28s 1.7s 2.69s 1.96s 1.9s 1.14s Lewis-Wester test M1 (26x26 sparse, det). 0.055s 0.064s 0.105s 0.093s 0.07s 0.049s Lewis-Wester test M2 (101x101 sparse, det). 264.99s 247.25s ---- 219.45s 304.25s 325.45s Lewis-Wester test N (poly at rational fcns). 205.08s 219.29s ---- 186.6s 242.13s 236.26s Lewis-Wester test O1 (three 15x15 dets)... (average) 7.95s 9.32s 16.14s 9.23s 10.0s 9.54s Lewis-Wester test P (det of sparse rank 101). 0.289s 0.24s 0.35s 0.38s 0.38s 0.3s Lewis-Wester test P' (det of less sparse rank 101). 0.78s 0.96s 1.46s 1.35s 1.16s 0.68s Lewis-Wester test Q (charpoly(P)). 16.54s 19.18s 31.04s 25.22s 24.01s 14.29s Lewis-Wester test Q' (charpoly(P')). 33.75s 41.05s 64.28s 49.95s 51.62s 27.46s computation of antipodes in Yukawa theory...... (total) 8.27s 10.4s 18.52s 12.54s 11.51s 7.15s Fateman's polynomial expand benchmark. 28.84s 28.29s 38.86s 31.72s 41.8s 41.17s Cheers -richy. -- Richard B. Kreckel <Richard.Kreckel(a)GiNaC.DE> <http://www.ginac.de/~kreckel/>

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Problems with linking GiNaC
by paul81＠webb.de 24 Sep '03

24 Sep '03

Hello, I'm new to GiNaC. In fact I've just installed the Debian package. But when I tried to compile the examples given in the section "A Tour of GiNaC" in the info pages it won't work. The object file is correctly made; but the linking process just returns a lot of errors. I used the command g++ $(ginac-config --libs) example.c++ ld returns many error messages (too much to send them). Basicly there two types. First many messages like example.o(.text+0x47): In function `main': : undefined reference to `GiNaC::symbol::symbol[in-charge](std::basic_string<char, std::char_traits<char>, std::allocator< char> > const&)' And for (I think) every reference in the object file. And second there also messages like: /usr/lib/libginac.so: undefined reference to `cerr' /usr/lib/libginac.so: undefined reference to `cln::compare(cln::cl_R const &, cln::cl_R const &)' (Very much of them, too). I have checked ginac-config. It seems to report the right libraries. When I tried static linking some of the messages disappeared, but only a few. Can anyone tell me, how I can get those examples run? Thank in advance, Paul PS: My systems configuration: g++ (GCC) 3.2.3 20030309 (Debian prerelease) GiNaC 1.0.11-1 (the debian packages: libginac-dev 1.0.11-1 & libginac0 1.0.11-1) CLN 1.1.5-1 (Debian: libcln2 1.1.5-1) and Debian GNU/Linux 2.4.17

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